# UNIFIED SCREW THREADS AND TOLERANCES CALCULATOR (INCH)

Unified screw threads and tolerances calculator was developed to calculate basic major, minor and pitch diameters of the external (bolt) and internal (nut) inch thread according to ASME B1.1-2003 standard. In addition to basic size calculations, limits of sizes calculations of different tolerance classes can be done according to same standard.

Calculator covers :

- UN and UNR thread forms

- Standard series of UNC, UNF, UNEF, UN-4, UN-6, UN-8, UN-12, UN-16, UN-20, UN-28 and UN-32.

- Tolerance classes of 1A, 2A and 3A for bolts and 1B, 2B and 3B for nuts

- Thread size from 0.0600 inch to 2 inches

Calculations can be done by selecting a desired thread size from a list of thread sizes which are in the diameter range from 0.060 inch to 2 inches. Bolt and nut tolerance classes can be selected among the alternatives 1A, 2A, 3A and 1B, 2B and 3B respectively. Class 2A and Class 2B are selected classes for commercial external and internal threads in ASME B1.1-2003. The user shall use class 2A for bolts and 2B for nuts unless there is a specific requirement to use other tolerance classes.

Dimensions given by this calculator are at 68 °F per ASME B1.1 standard.

Unified inch screw threads basic profile is shown in the following figure.  For the design profile,  see the "General Information" section.

 Unified inch screw thread (UN and UNR) basic profile according to ASME B1.1-2003

##### Calculator:

 INPUT PARAMETERS Nominal Size in Inches and Threads per Inch 0-80 1-64 1-72 2-56 2-64 3-48 3-56 4-40 4-48 5-40 5-44 6-32 6-40 8-32 8-36 10-24 10-32 12-24 12-28 12-32 1/4-20 1/4-28 1/4-32 5/16-18 5/16-20 5/16-24 5/16-32 3/8-16 3/8-20 3/8-24 3/8-28 3/8-32 7/16-14 7/16-16 7/16-20 7/16-28 7/16-32 1/2-13 1/2-16 1/2-20 1/2-28 1/2-32 9/16-12 9/16-16 9/16-18 9/16-20 9/16-24 9/16-28 9/16-32 5/8-11 5/8-12 5/8-16 5/8-18 5/8-20 5/8-24 5/8-28 5/8-32 11/16-12 11/16-16 11/16-20 11/16-24 11/16-28 11/16-32 3/4-10 3/4-12 3/4-16 3/4-20 3/4-28 3/4-32 13/16-12 13/16-16 13/16-20 13/16-28 13/16-32 7/8-9 7/8-12 7/8-14 7/8-16 7/8-20 7/8-28 7/8-32 15/16-12 15/16-16 15/16-20 15/16-28 15/16-32 1-8 1-12 1-16 1-20 1-28 1-32 1 1/16-12 1 1/16-16 1 1/16-18 1 1/8-7 1 1/8-8 1 1/8-12 1 1/8-16 1 1/8-18 1 1/8-20 1 1/8-28 1 3/16-12 1 3/16-16 1 3/16-18 1 1/4-7 1 1/4-8 1 1/4-12 1 1/4-16 1 1/4-18 1 1/4-20 1 1/4-28 1 5/16-12 1 5/16-16 1 5/16-18 1 3/8-6 1 3/8-8 1 3/8-12 1 3/8-16 1 3/8-18 1 3/8-20 1 3/8-28 1 7/16-12 1 7/16-16 1 7/16-18 1 1/2-6 1 1/2-8 1 1/2-12 1 1/2-16 1 1/2-18 1 1/2-20 1 1/2-28 1 9/16-16 1 9/16-18 1 5/8-8 1 5/8-12 1 5/8-16 1 5/8-18 1 5/8-20 1 11/16-16 1 11/16-18 1 3/4-5 1 3/4-6 1 3/4-8 1 3/4-12 1 3/4-16 1 3/4-20 1 13/16-16 1 7/8-6 1 7/8-8 1 7/8-12 1 7/8-16 1 7/8-20 1 15/16-16 2-4.5 2-6 2-8 2-12 2-16 2-20 External Thread (Bolt) Tolerance Class * 1A 2A 3A Internal Thread (Nut) Tolerance Class ** 1B 2B 3B

###### Note : ** 2B is normally selected for commercial internal (nut) threads. Use this tolerance class for commercial internal (nut) threads.

 RESULTS Parameter Symbol Value Unit Nominal Size -- --- --- Threads per inch -- --- Tolerance Class for External Thread -- --- Tolerance Class for Internal Thread -- --- Series Designation -- --- LIMITS OF SIZES FOR EXTERNAL THREADS (BOLTS) Allowance es --- inch Maximum Major Diameter dmax --- Minimum Major Diameter dmin --- Maximum Pitch Diameter d2max --- Minimum Pitch Diameter d2min --- UNR Maximum Minor Diameter d3max --- LIMITS OF SIZES FOR INTERNAL THREADS (NUTS) Minimum Major Diameter Dmin --- inch Maximum Pitch Diameter D2max --- Minimum Pitch Diameter D2min --- Maximum Minor Diameter D1max --- Minimum Minor Diameter D1min --- BASIC DIMENSIONS Basic Major Diameter d , D --- inch Basic Pitch Diameter d2 , D2 --- Basic Minor Diameter d1 , D 1 --- UNR Reference Minor Diameter  for External threads d3 --- Fundamental Triangle Height H --- Lead Angle at Basic Pitch Dia. λ --- ---

##### Definitions:

Design Profile: The shapes of the external and internal threads in which the limits of dimensions are applied.

Gages and Gauging : Specifications and dimensions for the gages used on Unified inch screw thread is defined in the ANSI/ASME B1.2-1983 standard. Types of gages including thread plug gages, snap gages, thread ring gages and plain diameter gages for internal and external threads are covered in same standard. Screw thread gauging systems for acceptability is covered in the ASME B1.3-2007 standard.

Major Diameter: The maximum diameter of a thread which is diameter of the crest of a male thread or root of a female thread.

Minor Diameter: The minimum diameter of a thread which is diameter of the root of a male thread or crest of a female thread.

Unified Screw Thread: A thread form used by the United Kingdom, Canada, and the United States to obtain screw thread interchangeability among these three nations. It has 60° thread angle and dimensions are stated in inch units.

UN form screw threads: The UN thread is intended for general purpose fastening operations.

UNC (Unified National Coarse): Most commonly used type for general engineering applications. This thread form is used in materials with low tensile strength which makes threads more resistance against stripping (internal threads) .UNC give possibility for quick assembly.

UNF (Unified National Fine): External threads of this Fine Series have greater tensile stress area than comparable sizes of the Coarse series. The Fine series is suitable when the resistance to stripping of both external and mating internal threads equals or exceeds the tensile load carrying capacity of the externally threaded member. It is also used where the length of engagement is short, where a smaller lead angle is desired, where the wall thickness demands a fine pitch, or where finer adjustment is needed.

UNEF (Unified National Extra Fine): Used when finer pitches than UNF are needed (Ex: Short engagement length).

UNS (Unified National Special): UNS are special series. Bolt / screw selection shall be done from standard series unless there is a special requirement to use a special series.

Thread class: A classification system to classify the threads for interchangeability and manufacturability. Class 1 threads are loosely fitting thread and used for ease of assembly. Most commonly used class is 2 and this class is designed for general use. Class 3 is used for closer tolerances.

##### General Information:

Some general information about the unified inch screw threads is listed in this section.

- The design profile of the unified screw thread form for classes 1A, 2A, 1B, and 2B is shown in the following figure. Refer to ASME 1.1:2003 standard for the profile of class 3A and class 3B.

 Unified inch screw thread (UN and UNR) design profile for classes 1A, 2A, 1B, and 2B according to ASME B1.1-2003

- ASME B1.1-2003 standard covers for UN and UNR thread forms with sizes from 0.0600 inch to 6 inch.

- The difference between UN and UNR thread forms is the form of root section. For UN thread form , the root of the thread is flat. Optionally a rounded root contour is allowed. For UNR, the root of the thread is only rounded root contour. UNR thread form is applicable to external threads only. UNR internal thread does not exist.

- The design profiles of external thread of UN and UNR screw is flat according to standard but it’s allowed to have some corner radius as shown in the figure. The same situation is valid for root of the internal threads.

- Standard series is given in the standard screw thread series table for information.

- The basic profile of UN, UNR and ISO profiles are same .

- Unified thread form and ISO metric form are not interchangeable

- In case to determine the thread pitch quickly, tools named thread pitch gauges can be used to find the pitch of the internal and external threads. Thread gauges are not used for precise measurements but allows user to determine thread pitch without losing time.

##### List of Equations:

 Parameter/Condition Symbol Equation Height of fundamental triangle H Thread basic pitch diameter d2, D2 Thread basic minor diameter d1, D1 External thread maximum major diameter dmax External thread minimum major diameter dmin External thread maximum pitch diameter d2max External thread minimum pitch diameter d2min External thread UNR reference minor diameter d3 External thread UNR maximum minor diameter d3max Internal thread minimum major diameter Dmin Internal thread maximum pitch diameter D2max Internal thread minimum pitch diameter D2min Internal thread maximum minor diameter D1max Internal thread minimum minor diameter D1min

 List of Parameters Symbol Definition es Allowance Td Major diameter tolerance of external thread Td2 Pitch diameter tolerance of external thread TD1 Minor diameter tolerance of internal thread TD2 Pitch diameter tolerance of internal thread

##### Reference:

• ASME B1.1-2003, Unified Inch Screw Threads (UN and UNR Thread Form)
• Oberg, E. , Jones ,F.D. , Horton H.L. , Ryffel H.H., (2016) . Machinery's Handbook . 30th edition.  Industrial Press Inc.
• Oberg, E. , Jones ,F.D. , Horton H.L. , Ryffel H.H., (2012) . Machinery's Handbook . 29th edition.  Industrial Press Inc.